Question

Determine k so that the given function has the given binomial factor
(12x^3+kx^2-80x-64) (x-2)

Answer 1

let R(x) be such function. By Remainder theorem, we know that for that to happen,
R(2)=0
12(2)^3+k(2)^2-80(2)-64=0
96+4k-224=0
4k=128
k=32